Analysis of the SOR iteration for the 9-point Laplacian
SIAM Journal on Numerical Analysis
Introduction to Parallel & Vector Solution of Linear Systems
Introduction to Parallel & Vector Solution of Linear Systems
On parallel methods for boundary value ODEs
Computing - Special issue on archives for informatics and numerical computation
SIAM Journal on Scientific and Statistical Computing
Parallel factorizations for tridiagonal matrices
SIAM Journal on Numerical Analysis
Boundary value methods and BV-stability in the solution of initial value problems
Applied Numerical Mathematics - Special issue: parallel methods for ordinary differential equations
A parallel preconditioning technique for boundary value methods
Applied Numerical Mathematics
Stability properties of some boundary value methods
Applied Numerical Mathematics
Boundary value methods based on Adams-type methods
NUMDIFF-7 Selected papers of the seventh conference on Numerical treatment of differential equations
A parallel Gauss-Seidel method for block tridiagonal linear systems
SIAM Journal on Scientific Computing
Convergence and stability of boundary value methods for ordinary differential equations
Proceedings of the 6th international congress on Computational and applied mathematics
A distributed memory parallel Gauss-Seidel algorithm for linear algebraic systems
Computers & Mathematics with Applications
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A parallel variant of the block Gauss-Seidel iteration for the solution of block-banded linear systems is presented. The coefficient matrix is partitioned among the processors as in the domain decomposition methods and then it is split so that the resulting iterative method has the same spectral properties of the block Gauss-Seidel iteration. The parallel algorithm is applied to the solution of block-banded linear systems arising from the numerical discretization of initial value problems by means of Boundary Value Methods (BVMs). BVMs define a new approach for the solution of ordinary differential equations and seem to be attractive for their interesting stability properties and a possible parallel implementation. In this paper, we refer to BVMs based on the extended trapezoidal rules.